Wednesday, May 21, 2025

Meta-analysis using Cohen's d in Microsoft Excel, and Online calculator (Excel-based)

Meta-analysis using Cohen's d Usman Zafar Paracha 2.1108 Usman Zafar Paracha Usman Zafar Paracha M1 = mean of group 1 M1 = mean of group 1 M2 = mean of group 2 SDpooled = pooled s... M1 = mean of group 1M2 = mean of group 2SDpooled = pooled standard deviation =√(((n1-1).SD12+(n2-1).SD22)/n1+n2-2) Cohen's d Cohen's d Cohen's d (M1-M2)/SDpooled (M1-M2)/SDpooled (M1-M2)/SDpooled formula formula formula It is a standardized measure of effect size, used to indicate the difference between two means in terms of standard deviation. It helps you understand how big or small the difference is, regardless of the units of measurement. It is a standardized measure of effect size, used to indicate... It is a standardized measure of effect size, used to indicate the difference between two means in terms of standard deviation. It helps you understand how big or small the difference is, regardless of the units of measurement. illustration Patreon and LinkedIn links LinkedIn Profile /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile /uzparacha /uzparacha /uzparacha Patreon Then then then Usman Zafar Paracha 1 Usman Zafar Paracha Usman Zafar Paracha example example example Usman Zafar Paracha 2 Usman Zafar Paracha Usman Zafar Paracha Suppose we have this data Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.995 Usman Zafar Paracha Usman Zafar Paracha As 0.2 → small effect, 0.5 → medium effect, and 0.8 → large effect As 0.2 → small effect, 0.5 → medium effect, and 0.8 → large e... As 0.2 → small effect, 0.5 → medium effect, and 0.8 → large effectSo, slightly medium (0.45) to large (1.2) effect size can be found Excel example data Usman Zafar Paracha 4 Usman Zafar Paracha Usman Zafar Paracha Excel example cohen's d d is Cohen’s d d is Cohen’s d n1 and n2 are the sample sizes of the two groups d is Cohen’s dn1 and n2 are the sample sizes of the two groups Variance of d Variance of d Variance of d Var(d) = (n1 + n2) / (n1 * n2) + (d²) / [2 * (n1 + n2)] Var(d) = (n1 + n2) / (n1 * n2) + (d²) / [2 * (n1 + n2)] Var(d) = (n1 + n2) / (n1 * n2) + (d²) / [2 * (n1 + n2)] formula.1012 formula formula The variance of Cohen's d is an important quantity when you're conducting meta-analyses or statistical inference based on Cohen’s d (standardized mean difference). The variance of Cohen's d is an important quantity when you'r... The variance of Cohen's d is an important quantity when you're conducting meta-analyses or statistical inference based on Cohen’s d (standardized mean difference).It shows how much the Cohen’s d estimate may fluctuate. illustration.1015 Patreon and LinkedIn links.1016 LinkedIn Profile.1017 /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile.1019 /uzparacha /uzparacha /uzparacha Patreon Then.1021 then then Usman Zafar Paracha 1.1022 Usman Zafar Paracha Usman Zafar Paracha example.1023 example example Usman Zafar Paracha 2.1024 Usman Zafar Paracha Usman Zafar Paracha Suppose we have this data.1025 Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.1026 Usman Zafar Paracha Usman Zafar Paracha Smaller variance means more precise (less uncertain / less variable) effect size estimate. The meta-analysis "trusts" or "relies on" more precise studies more heavily. The studies with smaller variances will carry more weight in the combined estimate of Smaller variance means more precise (less uncertain / less va... Smaller variance means more precise (less uncertain / less variable) effect size estimate. The meta-analysis "trusts" or "relies on" more precise studies more heavily. The studies with smaller variances will carry more weight in the combined estimate of effect size.Larger variance means less precise (more uncertain / more variable) effect size estimate. The studies with larger variances will carry less weight. Excel example data_1 Usman Zafar Paracha 4.1028 Usman Zafar Paracha Usman Zafar Paracha NORM.DIST Function.1029 Excel example variance d w_i is the weight assigned to the ith study, w_i is the weight assigned to the ith study, d_i is the effec... w_i is the weight assigned to the ith study,d_i is the effect size estimate from the ith study,Var(d_i) is the variance of the effect size estimate d_i Weight for Each Study Weight for Each Study Weight for Each Study w_i = 1 / Var(d_i) w_i = 1 / Var(d_i) w_i = 1 / Var(d_i) formula.1054 formula formula It shows weight for each study. It shows weight for each study. In this case, inverse-varianc... It shows weight for each study.In this case, inverse-variance weighting method has been used as it gives more weight to studies with smaller variance (i.e., more precise estimates). illustration.1057 Patreon and LinkedIn links.1058 LinkedIn Profile.1059 /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile.1061 /uzparacha /uzparacha /uzparacha Patreon Then.1063 then then Usman Zafar Paracha 1.1064 Usman Zafar Paracha Usman Zafar Paracha example.1065 example example Usman Zafar Paracha 2.1066 Usman Zafar Paracha Usman Zafar Paracha Suppose we have this data.1067 Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.1068 Usman Zafar Paracha Usman Zafar Paracha Higher weight (e.g., 107.14) means the study’s estimate has a smaller variance (more precise), so it will have a greater impact on the combined or pooled effect size. This study contributes more than twice as much as the study with weight 43.80 to the fi Higher weight (e.g., 107.14) means the study’s estimate has a... Higher weight (e.g., 107.14) means the study’s estimate has a smaller variance (more precise), so it will have a greater impact on the combined or pooled effect size. This study contributes more than twice as much as the study with weight 43.80 to the final meta-analysis estimate.Lower weight (e.g., 43.80) means the study’s estimate is less precise (larger variance), so it has less influence on the pooled estimate. Excel example data_2 Usman Zafar Paracha 4.1070 Usman Zafar Paracha Usman Zafar Paracha NORM.DIST Function.1071 Excel example weight w_i is the weight assigned to the ith study (often the inverse of its variance), w_i is the weight assigned to the ith study (often the invers... w_i is the weight assigned to the ith study (often the inverse of its variance),d_i is the effect size estimate from the ith study Weighted Effect Weighted Effect Weighted Effect w_i * d_i w_i * d_i w_i * d_i formula.1075 formula formula It refers to the contribution of each study’s effect size to the pooled (overall) effect, adjusted by its weight. It refers to the contribution of each study’s effect size to ... It refers to the contribution of each study’s effect size to the pooled (overall) effect, adjusted by its weight. illustration.1078 Patreon and LinkedIn links.1079 LinkedIn Profile.1080 /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile.1082 /uzparacha /uzparacha /uzparacha Patreon Then.1084 then then Usman Zafar Paracha 1.1085 Usman Zafar Paracha Usman Zafar Paracha example.1086 example example Usman Zafar Paracha 2.1087 Usman Zafar Paracha Usman Zafar Paracha Suppose we have this data.1088 Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.1089 Usman Zafar Paracha Usman Zafar Paracha Negative outcomes favor control (e.g., worse outcome), and Positive outcomes favor treatment (e.g., better outcome). Negative outcomes favor control (e.g., worse outcome), and Po... Negative outcomes favor control (e.g., worse outcome), and Positive outcomes favor treatment (e.g., better outcome).Larger absolute values show greater influence on the overall meta-analytic effect size. Excel example data_3 Usman Zafar Paracha 4.1091 Usman Zafar Paracha Usman Zafar Paracha NORM.DIST Function.1092 Excel example weighted effect d_pooled: the pooled or combined effect size estimate. d_pooled: the pooled or combined effect size estimate. d_i: t... d_pooled: the pooled or combined effect size estimate.d_i: the effect size from the i-th study.w_i: the weight of the i-th study (usually the inverse of the variance of d_i, i.e., w_i = 1 / Var(d_i)). Pooled Effect Size (Fixed Effects Model) Pooled Effect Size (Fixed Effects Model) Pooled Effect Size (Fixed Effects Model) d_pooled = (∑ w_i * d_i) / ∑ w_i d_pooled = (∑ w_i * d_i) / ∑ w_i d_pooled = (∑ w_i * d_i) / ∑ w_i formula.1096 formula formula The Pooled Effect Size (Fixed Effects Model) is a way to combine results from multiple studies (typically in a meta-analysis) into a single summary effect size, assuming that all studies share a common true effect size. That is, the variation between stu The Pooled Effect Size (Fixed Effects Model) is a way to comb... The Pooled Effect Size (Fixed Effects Model) is a way to combine results from multiple studies (typically in a meta-analysis) into a single summary effect size, assuming that all studies share a common true effect size. That is, the variation between studies is assumed to be due only to sampling error (not due to true differences in effect sizes across studies). illustration.1099 Patreon and LinkedIn links.1100 LinkedIn Profile.1101 /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile.1103 /uzparacha /uzparacha /uzparacha Patreon Then.1105 then then example.1107 example example Suppose we have this data.1109 Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.1110 Usman Zafar Paracha Usman Zafar Paracha The pooled effect size of –0.6805 indicates a moderate to large negative effect across the included studies. The pooled effect size of –0.6805 indicates a moderate to lar... The pooled effect size of –0.6805 indicates a moderate to large negative effect across the included studies.A negative value suggests that the treatment or condition being studied consistently shows a negative impact or effect compared to the control or baseline group. Excel example data.223 Usman Zafar Paracha 4.1112 Usman Zafar Paracha Usman Zafar Paracha NORM.DIST Function.1113 Excel example pooled effect size Usman Zafar Paracha 2.1114 Usman Zafar Paracha Usman Zafar Paracha w_i = weight assigned to the i-th study's effect size, often w_i = weight assigned to the i-th study's effect size, often ... w_i = weight assigned to the i-th study's effect size, oftenw_i = 1 / Var(d_i)∑ w_i = sum of all study weightsd_pooled = the weighted average of individual effect sizes d_i Variance of Pooled Effect Size Variance of Pooled Effect Size Variance of Pooled Effect Size Var(d_pooled) = 1 / ∑ w_i Var(d_pooled) = 1 / ∑ w_i Var(d_pooled) = 1 / ∑ w_i formula.1118 formula formula The variance of pooled effect size shows how uncertain or “spread out” that estimate is. The variance of pooled effect size shows how uncertain or “sp... The variance of pooled effect size shows how uncertain or “spread out” that estimate is.This shows the certainty of average effect after combining multiple studies. illustration.1121 Patreon and LinkedIn links.1122 LinkedIn Profile.1123 /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile.1125 /uzparacha /uzparacha /uzparacha Patreon Then.1127 then then example.1128 example example Suppose we have this data.1129 Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.1130 Usman Zafar Paracha Usman Zafar Paracha A smaller variance indicates that the pooled effect size estimate is relatively precise — there is less variability or uncertainty around the average effect. Conversely, a larger variance means more uncertainty. A smaller variance indicates that the pooled effect size esti... A smaller variance indicates that the pooled effect size estimate is relatively precise — there is less variability or uncertainty around the average effect. Conversely, a larger variance means more uncertainty.A low variance suggests confidence in the pooled effect size, meaning the studies generally agree on the size of the effect. Excel example data.228 Usman Zafar Paracha 4.1132 Usman Zafar Paracha Usman Zafar Paracha NORM.DIST Function.1133 Excel example variance of pooled effect size Usman Zafar Paracha 2.1135 Usman Zafar Paracha Usman Zafar Paracha Mean d is the overall mean effect size (e.g., Cohen's d) across all studies included in the meta-analysis. Mean d is the overall mean effect size (e.g., Cohen's d) acro... Mean d is the overall mean effect size (e.g., Cohen's d) across all studies included in the meta-analysis.SE is the standard error of the mean effect size estimate. Z Z Z Z = Mean d / SE Z = Mean d / SE Z = Mean d / SE formula.1139 formula formula It is used to test the significance of the overall effect size estimate. It is used to test the significance of the overall effect siz... It is used to test the significance of the overall effect size estimate. illustration.1141 Patreon and LinkedIn links.1142 LinkedIn Profile.1143 /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile.1145 /uzparacha /uzparacha /uzparacha Patreon Then.1147 then then example.1148 example example Suppose we have this data.1149 Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.1150 Usman Zafar Paracha Usman Zafar Paracha A large absolute value of Z indicates that the mean effect size is significantly different from zero. A large absolute value of Z indicates that the mean effect si... A large absolute value of Z indicates that the mean effect size is significantly different from zero.You can compare this Z-value against a standard normal distribution to get a p-value. Excel example data_4 Usman Zafar Paracha 4.1152 Usman Zafar Paracha Usman Zafar Paracha NORM.DIST Function.1153 Excel example Z d_pooled: The pooled effect size estimate (for example, a standardized mean difference or Cohen's d combined across studies). d_pooled: The pooled effect size estimate (for example, a sta... d_pooled: The pooled effect size estimate (for example, a standardized mean difference or Cohen's d combined across studies).SE(d_pooled): The standard error of the pooled effect size estimate. This measures how much variability there is in the pooled estimate.Z: The critical value from the standard normal distribution for the desired confidence level (e.g., 1.96 for 95% confidence). Confidence Interval (CI) for a Pooled Effect Size Confidence Interval (CI) for a Pooled Effect Size Confidence Interval (CI) for a Pooled Effect Size CI = d_pooled ± Z × SE(d_pooled) CI = d_pooled ± Z × SE(d_pooled) CI = d_pooled ± Z × SE(d_pooled) formula.1158 formula formula It is a way to express the uncertainty around the estimated overall effect size (often denoted as d_pooled) that comes from combining multiple studies (like in meta-analysis). It is a way to express the uncertainty around the estimated o... It is a way to express the uncertainty around the estimated overall effect size (often denoted as d_pooled) that comes from combining multiple studies (like in meta-analysis). illustration.1160 Patreon and LinkedIn links.1161 LinkedIn Profile.1162 /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile.1164 /uzparacha /uzparacha /uzparacha Patreon Then.1166 then then example.1167 example example Suppose we have this data.1168 Suppose we have this data Suppose we have this data Usman Zafar Paracha 2.1169 Usman Zafar Paracha Usman Zafar Paracha This means you are 95% confident that the true effect size lies between -0.79605 and -0.56503. This means you are 95% confident that the true effect size li... This means you are 95% confident that the true effect size lies between -0.79605 and -0.56503.Since both the lower and upper bounds are negative, this indicates a statistically significant negative effect. Excel example data_5 Usman Zafar Paracha 4.1171 Usman Zafar Paracha Usman Zafar Paracha NORM.DIST Function.1172 Excel example CI
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Monday, May 19, 2025

Cohen's d in Microsoft Excel, and Online calculator (Excel-based)

Cohen's d M1 = mean of group 1 M1 = mean of group 1 M2 = mean of group 2 SDpooled = pooled s... M1 = mean of group 1M2 = mean of group 2SDpooled = pooled standard deviation = √((SD12+SD22)/2) NORM.DIST Function Cohen's d Cohen's d (M1-M2)/SDpooled (M1-M2)/SDpooled (M1-M2)/SDpooled formula formula formula It is a standardized measure of effect size, used to indicate the difference between two means in terms of standard deviation. It helps you understand how big or small the difference is, regardless of the units of measurement. It is a standardized measure of effect size, used to indicate... It is a standardized measure of effect size, used to indicate the difference between two means in terms of standard deviation. It helps you understand how big or small the difference is, regardless of the units of measurement. gives gives gives illustration Patreon and LinkedIn links LinkedIn Profile /usmanzafarparacha /usmanzafarparacha /usmanzafarparacha LinkedIn Patreon profile /uzparacha /uzparacha /uzparacha Patreon Then then then Usman Zafar Paracha 1 Usman Zafar Paracha Usman Zafar Paracha Usman Zafar Paracha 4 Usman Zafar Paracha Usman Zafar Paracha example example example Usman Zafar Paracha 2 Usman Zafar Paracha Usman Zafar Paracha Suppose we have this data Suppose we have this data Suppose we have this data Excel example data Usman Zafar Paracha 2.995 Usman Zafar Paracha Usman Zafar Paracha Excel example formula Excel example outcome As 0.2 → small effect, 0.5 → medium effect, and 0.8 → large effect As 0.2 → small effect, 0.5 → medium effect, and 0.8 → large e... As 0.2 → small effect, 0.5 → medium effect, and 0.8 → large effectSo, –0.506 indicates a medium effect size, meaning there’s a moderate difference between the two groups.
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